#helped seeked from http://jackman.stanford.edu/classes/350B/10/prImage.pdf
library(biOps)
files <- (Sys.glob("Dropbox/Semester6/ai_cs365/hw2/jpg/*.jpg"))
z<-list()
y=""
output<-matrix(,,)
for (i in c(1:length(files))){
  y<-readJpeg(files[1])
  x<-readJpeg(files[i])     #all jpeg files in the folder are read
  
  x<-imgGreenBand(x)        #image converted to grayscale

  x<-as.vector(t(x))
  z[[i]]<-x
  
}
output = do.call(cbind,z)
output_inv = t(output)
r<-cor(output)

lambda <-eigen(r)$values
plot(y=lambda,x=1:length(lambda),log="x", las=1, ylab="eignevalues", xlab="Index")

std<-function(x){
  y<-matrix(c(0,255),2,1)   #checks for the values to be the range (0,255)
  A<- cbind(range(x),1)
  coefs <- solve(A,y)
  xmat<- cbind(x,1)
  z<- xmat%*%coefs
  z<-round(z)
  z[z<0]<-0
  z[z>255]<- 255
  z
}

reconstruct <- function(s,k=1){
                                    # reconstructes the image
  U<- s$u[,1:k]
  D<- matrix(0,k,k)
  diag(D)<-s$d[1:k]
  V<- s$v[,1:k]
  xhat <- U%*%D%*%t(V)
  z<- apply(xhat,1,std)
  return(t(z))
}
rmse <- function(y,z){          #error function
  e<- y-z
  return(sqrt(mean(e^2)))
}

s<-svd(output_inv)
#ksteps <- c(1:8)            

k=2       # number of principal components to take 

U<- s$u[,1:k]
D<- matrix(0,k,k)
diag(D)<-s$d[1:k]
V<- s$v[,1:k]
xhat <- U%*%D%*%t(V)
z<- apply(xhat,1,std)
z=t(z)




temp <- matrix(z[20,],nrow=576,ncol=720,byrow=TRUE)      # 20 is the number of image 25 in the imList
writeJpeg(filename="tmp25.jpg", imgdata=imagedata(temp))

temp <- matrix(z[5,],nrow=576,ncol=720,byrow=TRUE)      # 5 is the number of image 10 in the imList
writeJpeg(filename="tmp25.jpg", imgdata=imagedata(temp))